If \(x^4+x^2y^2+y^4=525\) and \(x^2+xy+y^2=21\), then find the value of \(x^2-xy+y^2\).
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 25
The expression \(x^4+x^2y^2+y^4\) is the product of the two expressions in the question: \(x^4+x^2y^2+y^4=(x^2+xy+y^2)(x^2-xy+y^2)\). So the required value is the first expression divided by the given factor.
\(x^4+x^2y^2+y^4=(x^2+y^2)^2-(xy)^2=(x^2+y^2+xy)(x^2+y^2-xy)\)
\(525=21\times(x^2-xy+y^2)\)
\(x^2-xy+y^2\displaystyle=\frac{525}{21}=25\)